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I have been doing a time series analysis of a PPP GDP with SPSS and I have tried to apply a Damped Trend method. This was a non-seasonal quarterly time series with a trend and as a result after using all of the models for exponential smoothing for non-seasonal time series the damped trend was the most precise one after comparing the basic RMSE, MAPE and MAE parameters and also when I compared it within ex ante analysis to a real data.

Problem is that when I check the different decomposed parameters of this time series, the trend is statistically insignificant on 95% interval... Can I still consider this damped trend method to be the best one or is it even as it should be that the trend becomes statistically insignificant ? Those are the model paramethers:

Exponential Smoothing Model Parameters

modelparams

Update

I have wrongly assumed the significance of Gamma(trend), is more than a 5%, it was a mistake.

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What you have there is complete nonsense.

Classically, exponential smoothing is not based on probabilistic models at all, and so there is no such thing as statistical significance.

It is possible to cast them into a context where they are the optimal forecast function for a certain probabilistic model (this was done decades later), but there the t-test for the trend coefficient is simply not valid because of the constraints on the coefficient (and your estimate is right on the upper boundary, as you can see).

As an aside, the trend parameter is reported as significant by your software, but this is largely irrelevant. Since you seem to be trying to forecast, what you should be using is out-of-sample forecasting accuracy.

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  • $\begingroup$ tongue in cheek do you mean to imply... pick that model that best predicts the out-of-sample values from 1 origin irrespective of model errors (sufficiency tests) in the fitting period or tests of statistical significance (necessity tests ) $\endgroup$
    – IrishStat
    May 5, 2018 at 18:31
  • $\begingroup$ @IrishStat I'm not sure where the "from 1 origin" bit is from, that's obviously wrong and I certainly didn't say that. What I am saying is that it is not at all necessary for a model to pass all those tests for it to be good for forecasting (particularly when the tests reported by the software are completely wrong, even if the model was exactly true, as above). $\endgroup$
    – Chris Haug
    May 5, 2018 at 18:49
  • $\begingroup$ I noticed right now that the trend parameter is significant anyways, I just misjudged the number... $\endgroup$ May 5, 2018 at 19:57

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